On the classification of automorphisms of trees

Authors

  • Samuel Coskey Boise State University
  • Kyle Beserra University of North Texas

DOI:

https://doi.org/10.11575/cdm.v14i1.62638

Abstract

We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the conjugacy problem in the case of automorphisms of several nonregularly branching trees.

References

\begin{thebibliography}{GNS01}

\bibitem[Bes16]{kyle-thesis}
Kyle Beserra.
\newblock On the conjugacy problem for automorphisms of trees.
\newblock Master's thesis, Boise State University, Boise, ID, 2016.

\bibitem[CE16]{ce1}
Samuel Coskey and Paul Ellis.
\newblock The conjugacy problem for automorphism groups of countable
homogeneous structures.
\newblock {\em MLQ Math. Log. Q.}, 62(6):580--589, 2016.

\bibitem[CES11]{ces}
Samuel Coskey, Paul Ellis, and Scott Schneider.
\newblock The conjugacy problem for the automorphism group of the random graph.
\newblock {\em Arch. Math. Logic}, 50(1-2):215--221, 2011.

\bibitem[DJK94]{dougherty-jackson-kechris}
R.~Dougherty, S.~Jackson, and A.~S. Kechris.
\newblock The structure of hyperfinite {B}orel equivalence relations.
\newblock {\em Trans. Amer. Math. Soc.}, 341(1):193--225, 1994.

\bibitem[FS89]{friedman-stanley}
Harvey Friedman and Lee Stanley.
\newblock A {B}orel reducibility theory for classes of countable structures.
\newblock {\em J. Symbolic Logic}, 54(3):894--914, 1989.

\bibitem[FW04]{foreman-weiss}
Matthew Foreman and Benjamin Weiss.
\newblock An anti-classification theorem for ergodic measure preserving
transformations.
\newblock {\em J. Eur. Math. Soc. (JEMS)}, 6(3):277--292, 2004.

\bibitem[Gao09]{gao}
Su~Gao.
\newblock {\em Invariant descriptive set theory}, volume 293 of {\em Pure and
Applied Mathematics (Boca Raton)}.
\newblock CRC Press, Boca Raton, FL, 2009.

\bibitem[GL16]{lupini-gardella}
Eusebio Gardella and Martino Lupini.
\newblock Conjugacy and cocycle conjugacy of automorphisms of {$\mathcal O_2$}
are not {B}orel.
\newblock {\em M\"unster J. Math.}, 9(1):93--118, 2016.

\bibitem[GNS01]{gawron}
Piotr~W. Gawron, Volodymyr~V. Nekrashevych, and Vitaly~I. Sushchansky.
\newblock Conjugation in tree automorphism groups.
\newblock {\em Internat. J. Algebra Comput.}, 11(5):529--547, 2001.

\bibitem[JKL02]{jackson-kechris-louveau}
S.~Jackson, A.~S. Kechris, and A.~Louveau.
\newblock Countable {B}orel equivalence relations.
\newblock {\em J. Math. Log.}, 2(1):1--80, 2002.

\bibitem[Kec92]{kechris-sections}
Alexander~S. Kechris.
\newblock Countable sections for locally compact group actions.
\newblock {\em Ergodic Theory Dynam. Systems}, 12(2):283--295, 1992.

\bibitem[Ser03]{serre}
Jean-Pierre Serre.
\newblock {\em Trees}.
\newblock Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003.
\newblock Translated from the French original by John Stillwell, Corrected 2nd
printing of the 1980 English translation.

\end{thebibliography}

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Published

2019-12-26

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Articles